01571nas a2200205 4500008004100000245006800041210006700109260001400176520091100190653002701101653003101128100002801159700001801187700003201205700002301237700002201260700002501282700002101307856003701328 2022 eng d00aMonitoring-induced Entanglement Entropy and Sampling Complexity0 aMonitoringinduced Entanglement Entropy and Sampling Complexity c1/29/20223 a

The dynamics of open quantum systems is generally described by a master equation, which describes the loss of information into the environment. By using a simple model of uncoupled emitters, we illustrate how the recovery of this information depends on the monitoring scheme applied to register the decay clicks. The dissipative dynamics, in this case, is described by pure-state stochastic trajectories and we examine different unravelings of the same master equation. More precisely, we demonstrate how registering the sequence of clicks from spontaneously emitted photons through a linear optical interferometer induces entanglement in the trajectory states. Since this model consists of an array of single-photon emitters, we show a direct equivalence with Fock-state boson sampling and link the hardness of sampling the outcomes of the quantum jumps with the scaling of trajectory entanglement.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aVan Regemortel, Mathias1 aShtanko, Oles1 aGarcĂ­a-Pintos, Luis, Pedro1 aDeshpande, Abhinav1 aDehghani, Hossein1 aGorshkov, Alexey, V.1 aHafezi, Mohammad uhttps://arxiv.org/abs/2201.1267201867nas a2200205 4500008004100000245006500041210006500106260001500171520119000186653003701376653004301413653002701456653003101483100001801514700002301532700002401555700002501579700002001604856003701624 2022 eng d00aSharp complexity phase transitions generated by entanglement0 aSharp complexity phase transitions generated by entanglement c12/20/20223 a

Entanglement is one of the physical properties of quantum systems responsible for the computational hardness of simulating quantum systems. But while the runtime of specific algorithms, notably tensor network algorithms, explicitly depends on the amount of entanglement in the system, it is unknown whether this connection runs deeper and entanglement can also cause inherent, algorithm-independent complexity. In this work, we quantitatively connect the entanglement present in certain quantum systems to the computational complexity of simulating those systems. Moreover, we completely characterize the entanglement and complexity as a function of a system parameter. Specifically, we consider the task of simulating single-qubit measurements of k--regular graph states on n qubits. We show that, as the regularity parameter is increased from 1 to n−1, there is a sharp transition from an easy regime with low entanglement to a hard regime with high entanglement at k=3, and a transition back to easy and low entanglement at k=n−3. As a key technical result, we prove a duality for the simulation complexity of regular graph states between low and high regularity.

10aComputational Complexity (cs.CC)10aFOS: Computer and information sciences10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aGhosh, Soumik1 aDeshpande, Abhinav1 aHangleiter, Dominik1 aGorshkov, Alexey, V.1 aFefferman, Bill uhttps://arxiv.org/abs/2212.1058201434nas a2200169 4500008004100000022001400041245009100055210006900146260001400215490000600229520089000235100001801125700002301143700002301166700002501189856005001214 2021 eng d a2691-339900aComplexity of Fermionic Dissipative Interactions and Applications to Quantum Computing0 aComplexity of Fermionic Dissipative Interactions and Application c9/17/20210 v23 a

Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state. This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing. We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter. We determine important classes of simulable and nonsimulable two-body dissipation. Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates. 

1 aShtanko, Oles1 aDeshpande, Abhinav1 aJulienne, Paul, S.1 aGorshkov, Alexey, V. uhttp://dx.doi.org/10.1103/PRXQuantum.2.030350